Karen White is trans. There is no way around that. White self identifies, has lived in role - intermittently, but Bunce does it once or twice a week when the mood strikes and has won a women's award - who knows what degree of dysphoria White does or doesn't suffer. It's irrelevant.
By Stonewall's standards, by the Prison authority standards, White was trans. Some rapists, sex offenders and dangerous people are going to be trans, the way some gay people are, some men are, some women are. Trans is never going to be a guaranteed way to prevent any sex offending - if it was then for God's sake we could just push this on the male population, encourage all of them to transition and male violence would end overnight.
White is trans. That's fine. White's fully entitled to be trans. So is anyone else. Their offending behaviour doesn't change their right to their own identity, gender expression, authentic self and all the rest of it. What White proves is that transwomen cannot be given open, free, self identified rein to walk into women's spaces because some will use that as a means to offending, and some offenders will see transition as a very useful means to offending. That harms everyone.
Third space.